Old thread, but always a current topic... I think there are differences between the Coupe trim levels, and between Genesis models, and of course, between manufacturers. The 2013 Coupes have a 3-stage system, but on my
2012 3.8 R-Spec it's a 2-stage.
On mine, the Stability (yaw) and Traction (wheelspin) ESC system is ON or OFF, while ABS is always on, except for the handbrake. When ESC is ON, the engine is slightly detuned or certainly more sluggish, with any hint of wheelspin handled using various levels of reactions, as we all know. Drifting or burning out is nearly impossible with the system ON. With ESC OFF, the R-Spec engine is tuned back up, drifts and burns are easy although tricky because of manual transmission, which is normal. Only when the system is OFF is the incredible balance of the R-Spec's handling revealed. It's just a very different car under hard driving, while at low speeds and light acceleration in dry conditions you can't really tell the difference between ON/OFF. I think of it as having "safe" vs "sport" modes.
The other models and/or years seem to be different in configuration, or perhaps the drivers who post on various forums like this, for fear of being attacked, are really unsure as to what is going on - many do not seem to race or even drive really hard.
The button is there for a reason. When driving hard, the ESC system can be as dangerous as the easy drifting from having it off under wide open throttle. It comes back to the driver and their level of experience. The R-Spec Coupe is designed to perform with cars costing two and three times more

More expensive "supercars" can have various modes and separate system controls for traction, stability and throttle response, etc.